Z Score to Percentile Calculator
Convert any z-score to its percentile, left-tail and right-tail probabilities — instantly, with the shaded bell curve showing the exact area. Free, no signup.
Convert z-score to percentile
Enter any z-score, positive or negative — e.g. 2.00 or −1.96.
The shaded region is the left-tail area — your percentile.
This z score to percentile calculator runs entirely in your browser. Nothing is uploaded or stored.
How the conversion works
To convert a z-score to a percentile, you find the cumulative probability — the total area under the standard normal curve to the left of that z-score — and multiply it by 100. That area is the percentile rank: it tells you what share of all values in a normal distribution fall at or below your score.
Picture the bell curve with your z-score marked on the horizontal axis. Everything under the curve to the left of that mark is one shaded region. For z = 1.64, that region covers 0.9495 of the total area — 94.95%. So a z-score of 1.64 is the 94.95th percentile: it beats roughly 95 out of every 100 values. For a negative z-score the same logic holds — z = −1.96 shades only 0.0250 of the area, giving the 2.50th percentile.
Before calculators, students did this lookup in a printed z score table: find the row and column for your z-score, read the left-tail probability, multiply by 100. The converter above does the same job with the full precision of the normal distribution — no rounding to four decimals, no misread rows.
One-tailed vs two-tailed — which probability do you need?
The calculator shows four numbers because "the probability" of a z-score depends on the question you are asking. A one-tailed probability measures the area in a single tail. If a researcher asks "what is the chance of scoring above z = 1.64?", the answer is the right-tail area: about 0.0505, or 5.05%. That is the number behind one-sided significance tests.
A two-tailed probability covers both extremes — the chance of a result at least this unusual in either direction. For z = 1.64 it is about 0.1010 (10.10%), simply double the one-tailed value, because the normal curve is symmetric. Two-tailed probabilities are the default in most hypothesis testing: a "p-value" for a z-test is usually this two-tailed area.
Rule of thumb: if your question has a direction ("greater than", "at least this high"), use the one-tailed number. If it only cares about extremeness ("different from average", "unusual"), use the two-tailed number. Mixing them up is one of the most common errors in z score probability calculations — when in doubt, the shaded curve on the converter shows you exactly which area each number describes.
Worked examples
Example 1 — z = 1.64. The left-tail probability is 0.9495, so the percentile rank is the 94.95th percentile. The right-tail probability is 1 − 0.9495 = 0.0505: about a 5% chance of scoring higher. This is why 1.64 is the classic one-tailed 5% cutoff.
Example 2 — z = −1.96. The left-tail probability is 0.0250, giving the 2.50th percentile — only 2.5% of values fall below it. The two-tailed probability is 0.0500: values at least this extreme in either direction occur 5% of the time, which is exactly why ±1.96 anchors 95% confidence intervals.
Example 3 — z = 0. The left-tail probability is 0.5000, the 50th percentile — dead average, as expected. Sanity-checking with z = 0 is a good habit: if your converter does not return the 50th percentile there, something is wrong.
Critical values quick reference
These z critical values come up so often they are worth memorizing:
| Z-score | Percentile | One-tail area | Used for |
|---|---|---|---|
| 1.645 | 95.00th | 0.0500 | One-tailed 5% test |
| 1.96 | 97.50th | 0.0250 | Two-tailed 5% test, 95% CI |
| 2.576 | 99.50th | 0.0050 | Two-tailed 1% test, 99% CI |
Z-score to p-value: the same conversion
If you arrived here searching for a z score to p value conversion, good news: it is the same calculation. A p-value for a z-test is just a tail probability expressed as a decimal. For a one-tailed test, the p-value is the tail area the converter reports. For a two-tailed test, use the two-tailed number. And going the other direction — from a p-value back to a z-score — is what our percentile to z score calculator does: enter 97.5 as the percentile and you get z = 1.96, the familiar cutoff.
One caution: a p-value is not the probability that your hypothesis is true. It is the probability of seeing data this extreme if the null hypothesis were true. The conversion is pure arithmetic; the interpretation still needs care. And going the other direction — converting p value to z score — is what our percentile to z score calculator does: enter 97.5 as the percentile and you get z = 1.96, the familiar cutoff.
How to read the shaded curve
The converter draws the standard normal curve fresh for every z-score you enter. The horizontal axis is marked in standard deviations from the mean (μ = 0 at the center, ±1σ, ±2σ, ±3σ), and the red dashed marker shows exactly where your z-score sits. Everything shaded blue to the left of the marker is the left-tail area — the cumulative probability, which × 100 is your percentile.
Watch what happens as you type: nudge the z-score from 1.00 to 2.00 and the shaded region grows from 84.13% to 97.72% of the curve. Enter a negative value and the shading shrinks toward the left tail. This visual is the reason the curve beats a bare number — you see which area your percentile describes, so one-tailed and two-tailed mix-ups become almost impossible.
Frequently asked questions
How do I convert a z-score to a percentile?
Enter the z-score and find its left-tail probability — the area under the normal curve to the left of that value — then multiply by 100. A z-score of 1.64 has a left-tail probability of 0.9495, which is the 94.95th percentile. The calculator above does the conversion instantly and shades the exact area.
What percentile is a z-score of 2?
A z-score of 2.00 sits at the 97.72nd percentile: 97.72% of values in a normal distribution fall at or below it, and only about 2.28% score higher. It is a high but not extreme result — extreme territory starts around z = ±3.
What percentile is a z-score of 1.96?
A z-score of 1.96 corresponds to the 97.50th percentile, leaving exactly 2.5% in the upper tail. This is why ±1.96 is the standard cutoff for 95% confidence intervals and two-tailed hypothesis tests at the 5% significance level.
What is the difference between one-tailed and two-tailed probability?
A one-tailed probability measures the area in a single tail — for example, the chance of scoring above z = 1.64 (about 5%). A two-tailed probability doubles it, covering both extremes (about 10%). Use one-tailed when direction matters, two-tailed when any extreme counts.
Can a z-score be converted to a percentage?
Yes, with care: the percentile is already a percentage-style rank (97.72nd percentile). Do not confuse it with "percent correct" — a percentile tells you what share of the group you beat, not what fraction of questions you answered right.